номер 105 гдз 8 класс алгебра Муравин Муравин

1)\begin{equation}\frac{ax+b}{x+10}-\frac{x-5}{2x+20}=\frac{3x-5}{2\left ( x+10 \right )} \end{equation} \begin{equation}\frac{ax+b}{x+10}-\frac{x-5}{2\left ( x+10 \right )}= \end{equation} \begin{equation}=\frac{2ax+2b-x+5}{2\left ( x+10 \right )} \end{equation}
2ax + 2b - x + 5 = 3x - 5
b = -5  a = 2
2 · 2 · x + 2 · (-5) - x + 5 = 4x - 10 - x + 5 = 3x - 5
Ответ: b = -5  a = 2
2)\begin{equation}\frac{a}{x+3}+\frac{b}{x-3}=\frac{16x+18}{x^{2}-9} \end{equation} \begin{equation}\frac{a}{x+3}+\frac{b}{x-3}=\frac{ax-3a+bx+3b}{x^{2}-9} \end{equation}
ax - 3a + bx + 3b = 16x + 18
ax + bx = 16x
x(a + b) = 16x
a + b = 16
3b - 3a = 18
3(b - a) = 18
b - a = 6 \begin{equation}+\left\{\begin{matrix} a+b=16\\ b-a=6 \end{matrix}\right. \end{equation}
2b = 22
b = 11
11 - a = 6
11 - 6 = a
a = 5
Ответ: a = 5  b = 11
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